CN118033180A

CN118033180A - Method for measuring optical characteristics of sub-micron area of sample and atomic force microscope

Info

Publication number: CN118033180A
Application number: CN202410181480.XA
Authority: CN
Inventors: 王浩民; 徐晓纪
Original assignee: Lehigh University
Current assignee: Lehigh University
Priority date: 2018-01-22
Filing date: 2019-01-22
Publication date: 2024-05-14
Also published as: US20210041477A1; EP3743732A2; US20220390485A1; CN111886505A; WO2019144128A3; CN111886505B; US12000861B2; US11415597B2; EP3743732A4; WO2019144128A2

Abstract

Method for measuring optical properties of sub-micron regions of a sample and atomic force microscope. Conventional scattering microscopy (s-SNOM) techniques, using tap mode operation and lock-in detection, fail to provide direct tomography information with a well-defined tip-sample distance. PF-SNOM uses a peak force scattering scanning near field optical microscope in combination with peak force tapping mode and time-gated light detection, and can directly separate the perpendicular near field signal from the sample surface for three-dimensional near field imaging and spectroscopic analysis. The PF-SNOM also provides a spatial resolution of 5nm and can measure both mechanical and electrical properties as well as optical near field signals.

Description

Method for measuring optical characteristics of sub-micron area of sample and atomic force microscope

The present application is a divisional application of international application number PCT/US2019/014572, application date 2019, 1 month 22, and the chinese national phase application of PCT application entitled "non-tapping mode scattering scanning near field optical microscopy system and method", the application number 201980020933.8 of which is incorporated herein by reference in its entirety.

Priority claim

The present application claims priority from U.S. provisional application No. 62/620,263 entitled "non-tapping mode scattering scanning near field optical microscope with peak force tapping mode" filed on 1 month 22 of 2018, which is incorporated herein by reference in its entirety for all purposes.

Technical Field

The present disclosure relates to a method of measuring optical properties of a sub-micron region of a sample and an atomic force microscope.

Background

Scanning near field optical microscopy (SCANNING NEAR-Field Optical Microscopy, SNOM, also known as near field scanning optical microscopy-NSOM) is a microscopy technique used to conduct nanostructure studies. In SNOM (described below), the laser is focused through an aperture having a diameter smaller than the wavelength excited by the laser, which results in an evanescent field (or near field) being generated distally of the aperture. When scanning a sample at a short distance under an aperture, either transmitted or reflected light will be captured and displayed by the display device with a spatial resolution below the diffraction limit.

In SNOM applications, scattering scanning near-field optical microscopy (s-SNOM) is a special technique that has been developed to enable the study of various nanoscale phenomena that cannot be studied in far-field spectra due to their optical diffraction limits. s-SNOM has become a tool to study graphene plasmons, surface phonon polarons, phase changes of related electronic materials, components in heterogeneous materials, and chemical reactions. In s-SNOM, the elastically scattered light of a sharp metal tip operated by an atomic force microscope (atomic force microscope, AFM) over a sample is measured by an optical detector. Near field interactions between the tip and the sample can change the polarizability of the tip, thereby affecting the elastic scattering of light. However, since elastic scattering does not change the wavelength of the scattered light, reflected or scattered photons from other parts of the AFM cantilever or the sample surface outside the tip region will also be recorded by the same optical detector and result in a background signal, which is the far field background from the background region outside the tip-sample interaction region. To distinguish between far field background and near field signals of tip-sample interaction, one conventional approach is to oscillate the tip in tapping mode by mechanical resonance of the AFM cantilever and phase lock demodulate or fourier analyze the scattered light at a non-fundamental of the tip oscillation frequency.

Despite the wide application and success of this approach, phase lock detection in tapping mode s-SNOM still has limitations. First, because the phase-locked demodulated s-SNOM signal is a discrete value, conventional s-SNOM cannot provide direct information of the vertical extent of the tip-sample near field interaction. This results in a very complex and missing distance dependence of the tip-sample near field interaction in the signal generation mechanism. Second, s-SNOM signals of different demodulation orders exhibit different signal shapes and cause the spatial pattern to become blurred. Furthermore, s-SNOM operating in a tapping mode cannot be performed simultaneously with other AFM modes requiring firm tip-sample contact, such as measuring mechanical properties and conductivity. The s-SNOM of the tapping mode does not enable simultaneous and related measurements for near-field light, mechanical and electrical signals.

Disclosure of Invention

One aspect of the application relates to a method of measuring optical properties of a sub-micron region of a sample, the method using an atomic force microscope comprising: allowing the probe to interact with the sample; illuminating the sample with a beam of light from a radiation source such that light is scattered from the probe-sample interaction region; collecting scattered light from the probe-sample interaction region and a background region using a detector, the scattered light being a function of a distance between the probe and the sample; and constructing a near field signal in response to the collected scattered light relative to the distance; and wherein the vertical resolution of the near field signal is at least 7nm.

Another aspect of the application relates to an atomic force microscope for measuring optical properties of a sub-micron region of a sample, comprising: a probe for interacting with the sample; a radiation source for illuminating the sample with a beam of light such that light is scattered from the probe-sample interaction region; a detector for detecting scattered light from the probe-sample interaction region and a background region, the scattered light being a function of the distance between the probe and the sample; and a processor configured to construct a near field signal in response to the detected scattered light relative to the distance, and wherein a vertical resolution of the near field signal is at least 7nm.

Drawings

Embodiments of the presently disclosed subject matter will be described with reference to the drawings, in which:

FIG. 1 is a system diagram of a peak force scattering Near field optical microscope (PF-SNOM, peak Force Scattering-Type Near-Field Optical Microscopy) device in accordance with an embodiment of the presently disclosed subject matter;

FIG. 2A is a graph showing infrared detector signals of cantilever vertical deflection and scattered light from a tip of a needle recorded simultaneously by PF-SNOM technology in accordance with an embodiment of the presently disclosed subject matter;

FIG. 2B is a graph showing the relationship between the optical detector signal derived from the two waveforms in FIG. 2A and the tip-sample distance, with the background signal retained, in accordance with an embodiment of the presently disclosed subject matter;

FIG. 2C is a graph showing a pure near field signal with a clear tip-sample distance dependence obtained by subtracting the fitted linear background of FIG. 2B, in accordance with an embodiment of the presently disclosed subject matter;

FIG. 2D is a graph showing the homodyne phase dependence of a PF-SNOM signal in accordance with an embodiment of the presently disclosed subject matter;

FIG. 2E is a graph showing different PF-SNOM signals for different tip-sample distances relative to one wavelength (1405 cm ^-1) when a boron nitride nanotube is subjected to a 1000nm long line scan, in accordance with an embodiment of the presently disclosed subject matter;

FIG. 2F is a graph of boron nitride nanotubes performing the line scan of FIG. 2E according to an embodiment of the presently disclosed subject matter;

FIGS. 3A-3J are graphs showing PF-SNOM operations performed on boron nitride nanotubes and hexagonal boron nitride to reveal tip-induced phonon polarization damping, 5nm spatial resolution, and related mechano-electrical and near-field imaging, in accordance with embodiments of the presently disclosed subject matter;

FIG. 4 is a flow chart showing a method for implementing PF-SNOM techniques in an AFM microscope, in accordance with an embodiment of the presently disclosed subject matter; and

Fig. 5 is a diagram showing elements or components in a computer device or system configured to implement a method, process, function, or operation in accordance with an embodiment.

It should be noted that the same numbers used in the present invention and the figures denote similar components and features.

Detailed Description

The subject matter of the embodiments disclosed herein is described below in terms of meeting regulatory requirements, but such description is not intended to limit the scope of the claims. The claimed subject matter may also be implemented in other ways, may include different elements or steps, and may be used in conjunction with other present or future technologies. The following description should not be construed as implying any particular order or arrangement between various steps or elements unless the order of individual steps or elements is explicitly described.

Embodiments will be described more fully hereinafter with reference to the accompanying drawings, in which exemplary embodiments of the systems and methods described herein may be practiced. The systems and methods may, however, be implemented in many different ways and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable requirements and will be appreciated by those skilled in the art from a review of the scope of the subject matter.

In summary, the systems and methods discussed herein may be used directly with peak force scattering Near field optical microscopy (Peak Force Scattering-Type Near-Field Optical Microscopy, PF-SNOM). Unlike previous conventional approaches, the PF-SNOM technique avoids tapping mode operation, which can lead to subsequent information loss in lock detection. The new technology discussed herein combines a peak force tap (peak force tapping, PFT) mode with time-gated detection (time-detected detection) of near-field scattered signals using far-field background differential algorithm (subtraction algorithm). Compared to conventional tap-mode based s-SNOM, PF-SNOM is able to achieve a tomographic slice (tomographic sectioning) of a tip-sample near-field interaction at a well-defined tip-sample distance and simultaneously perform related near-field, mechanical, and electrical measurements with a high spatial resolution well below the diffraction limit. These aspects, as well as advantages and other aspects, are described in more detail in fig. 1-5 below.

Fig. 1 is a system diagram of a peak force (e.g., non-tapping mode) scattering near field optical microscopy (PF-SNOM) device 100 according to an embodiment of the presently disclosed subject matter. In this embodiment, the PF-SNOM device 100 includes an atomic force microscope (Atomic Force Microscope, AFM) 105 with a diode laser 110 (e.g., light source) to sense the deflection of the AFM cantilever 115 by reflection at the back of the cantilever and detection by a deflection detector 119. The apparatus is configured to allow a beam from a laser source (e.g., a frequency tunable mid-infrared Quantum Cascade Laser (QCL) 128) to be focused onto a sample (not shown) that may be placed on a sample stage 117 having a piezoelectric oscillator 118. The light source 128 may be an infrared laser adapted to produce a light beam having a wavelength in the infrared range, although other ranges may be used in other embodiments. In addition, the piezoelectric oscillator 118 arranged on the sample stage may be driven by a piezoelectric driving stage having a frequency between 0.1khz and 100.0khz, with 4.0khz being a typical driving frequency. In another embodiment, instead of oscillating the sample, the AFM cantilever may be oscillated at a non-resonant frequency between 0.1kHz and 100.0 kHz. Oscillation driven AFM cantilever 115 at a non-resonant frequency does not retain kinetic energy (KINETIC ENERGY), unlike a tap mode AFM that drives AFM cantilever 115 at or near the cantilever's mechanical resonance.

AFM 105 further includes a probe system having a driver 111 adapted to manipulate cantilever 115, cantilever 115 having a probe tip 116 (typically covered with a metal such as gold) at the end of cantilever 115. As with most AFMs, the cantilever is flexible and vibrates adjacent to a piezoelectric oscillator 118 disposed on the sample stage 117. Typically, when cantilever 115 is approaching or contacting a sample disposed on sample stage 117, cantilever 115 will deflect up and down when affected by the mechanical force generated by the sample on piezoelectric oscillator 118. The probe tip 116 may be placed near or in contact with the sample to measure deflection of the cantilever 115 over time using a deflection detector 119, as will be described in more detail below. The deflection measurements may be input to the processor 130 to determine sample information (e.g., analysis circuitry for analyzing the collected data).

In addition, light from the mid-infrared quantum cascade laser 128 is directed to the beam splitter 121. The frequency of the mid-infrared quantum cascade laser may be tuned and may provide a selective optical frequency (e.g., vibrational transitions, polarization modes, or other resonance phenomena of the molecules) that matches the resonance in the sample. The light source may also be another laser source providing a resonant frequency, for example, nonlinear optical frequency converted laser radiation used in an optical parametric oscillator. A portion of the laser light is split by beam splitter 121 into reference light field 124 and another portion from beam splitter 121 can be focused onto probe tip 116 by first parabolic mirror 120. The function of parabolic mirror 120 may be replaced by other types of light focusing optical elements, such as lenses. Light is scattered from the probe tip 116. Scattered light may reflect off of the sample. The first parabolic mirror 120 captures both the directly scattered light and the secondarily reflected light.

When light is reflected, the first parabolic mirror 120 directs it to the beam splitter 121. Additionally, a reference laser field 124 may also be added to the beam splitter 121 so that the signal may facilitate detection of the optical signal reflected by the needle tip by interferometric detection. To this end, the beam splitter 121 may direct the optical signal (a combination of the reflected signal from the sample and the reference signal 124) to a second parabolic mirror 122 (or equivalent focusing element, such as a lens) and may be detected by an optical detector 123 (e.g., mercury cadmium telluride (Mercury Cadmium Telluride, MCT) detector). It should be noted that the above arrangement comprising a light source (laser 128), a beam splitter 121, a light reference path 124, a light path containing a needle tip 116 and an optical detector 123 for interference detection is a typical arrangement of s-SNOM and is an asymmetric michelson interferometer (Michelson interferometer). The detected optical signals (e.g., scattered signals) may be sent to processor 130 and used with the deflection detected by deflection detector 119 of cantilever 115 to determine various aspects of the sample disposed on sample stage 117. As described below, fig. 2A shows the optical detector signal and cantilever vertical deflection signal measured over time. Also, the specific case of these measurements will be discussed further below. Next, the operation and details of the apparatus shown in fig. 1 will be presented with reference to the components of the apparatus 100 of fig. 1.

FIG. 2A is a graph 200 of simultaneous recording of vertical deflection 205 of cantilever 115 and scattered signal 207 of scattered light from needle tip 116 detected by optical detector 123 by PF-SNOM technology in accordance with an embodiment of the subject matter disclosed herein. During operation, cantilever 115 may remain stationary while a sample on sample stage 117 is vibrated vertically at a large amplitude (e.g., 300 nm) at a low frequency of several kilohertz (defined as the PF-SNOM frequency) by piezoelectric oscillator 118. For each oscillation cycle, the maximum cantilever deflection (e.g., peak force) may be controlled and maintained at the set point under the negative feedback loop. When the needle tip 116 approaches the sample surface, intermolecular attraction causes the needle tip 116 to jump and contact the sample surface, a phenomenon known as jump-in contact (snap-contact), also known as jump-contact. The tip-sample contact time is predetermined and the bounce contact time t _s in fig. 2A can be measured from the waveform of the cantilever deflection signal 205 and is consistent with the minimum deflection. In this example, the bump contact process (e.g., darker bands near t _s 210) lasts from about 45 to 52 μs, and the bump contact time t _s is 52 μs.

In fig. 2A, the bounce contact time t _s, the maximum peak force time t _p 212 and the tip separation time td 214 may be determined from the minimum and maximum deflection diagrams shown. The cantilever 115 at the top of fig. 2A shows the corresponding tip-sample configuration for three phases of the PF-SNOM cycle, from left to right: the tip approaches the sample 220, the runout contact 222, and the dynamic tip-sample contact 224 that allows for other AFM modalities, such as electrical measurement 230 (here exemplified by the voltage applied between the tip and the sample). A graph 208 of the detector signal (207 in fig. 2A) versus tip-sample distance (as shown in fig. 2B, which will be discussed below) can then be derived, giving the fact that the distance at the bounce contact time t _s can be defined as zero. The tip-sample distance may be positive before the bump contacts t _s 210,210. The distance remains zero from after the bump contact to before the tip is retracted from the sample after t _d, 214.

Fig. 2B is a graph 240 showing the relationship between the optical detector signal 208 derived from the two waveforms in fig. 2A and the tip-sample distance, with the far field background signal remaining unchanged, in accordance with an embodiment of the presently disclosed subject matter. In one embodiment, the cantilever vertical deflection waveform D (t) 205 and the scattered light detector signal waveform S (t) 207 in FIG. 2A (where t is time) are converted to a function S (D) 208 as shown in FIG. 2B, where D is the tip-sample distance for tomography. In PFT mode, the sample piezo-electric station may be driven vertically in sinusoidal oscillation at PFT frequency f. The vertical position d _z of the piezoelectric station can be expressed as:

Where A is the peak force amplitude, Is the oscillation phase of the piezoelectric station. In 205, the highest position of the piezo also corresponds to the maximum cantilever vertical deflection (peak force set point) at time t _p. At t _p, by/>Calculating the phase/>, of the movement of the piezoelectric stationTo derive the maximum value of dz and then derived as/>Thus, the vertical position dz of the press station is:

d_z(t)＝A cos(2πf(t-t_p))

In this example, the time of maximum cantilever bending t _p is identified from the cantilever vertical deflection signal waveform D (t) 205. From knowledge of the cantilever deflection sensitivity V, i.e. the correlation of the voltage or signal measured by the deflection sensor with the actual tip movement in nanometers (typically tens of nanometers), it is known that the tip-sample distance d (t) in the time domain is:

d(t)＝A-d_z(t)+V·D(t)

Or alternatively

d(t)＝A-Acos(2πf(t-t_p))+V·D(t)

Since the tip-sample distance is almost zero after the jumping contact time t _s and before the separation time t _d (considering that the effect of the indentation in PF-SNOM is negligible because the signal is not extracted in the indentation), one d (t) can be defined as two regions and given in truncated sinusoidal shape:

All t _p、t_s and t _d can be identified from the original D (t) curve 205. In the present PF-SNOM operation, only the light scattering signal S (t) 207 prior to the bounce contact time t _s is processed in each PFT cycle. Thus, from the calculated d (t) and the S (t) of t < t _s of the simultaneous measurement, a relationship between the scatter signal and the tip-sample distance S (d) 208 is derived.

A significantly increased scattered signal at the short tip-sample distance caused by the short near field interaction can be observed in fig. 2B, as well as a linear fitted long distance far field background 241 (dashed line). Since the PF-SNOM technique allows for large amplitude oscillations of the tip-sample distance without losing feedback stability, far field background 241 can be precisely linear fit within the region of the tip away from the sample, allowing for precise linear prediction of far field background signals at short tip-sample distances. To obtain a near-field scattered signal, the far-field background signal of the background region can be removed from the scattered light signal, since at larger tip-sample distances the change in detector signal is only responsive to the change in far-field scattering of the cantilever axis and the sample surface. Since the laser wavelength is about 3-12 μm, the variation of the sample stage vertical position is relatively small, and thus the variation of the far-field scattering signal can be approximated as a linear variation with respect to the tip-sample distance. The fitted linear far field background signal is then extrapolated to the short tip-sample distance region for removal from the detector signal. The resulting difference (fig. 2C) provides a relationship between the near field signal and the tip-sample distance, whereby the perpendicular near field response can be accessed accurately.

Fig. 2C is a graph 260 of a pure near field signal 261 with explicit distance dependence obtained by subtracting a fitted linear background 241 from the detector signal 208 of fig. 2B, according to an embodiment of the presently disclosed subject matter. Subtracting the near-linear far-field background from the scattered signal yields a pure near-field response as a function of distance. In one embodiment, the process for removing far-field signals includes analyzing the signals to linearly fit to the S (d) region of large tip-sample distance d shown in fig. 2B (e.g., 20nm or more on the right side of the figure). In another embodiment, a general trend fit may be used to account for slight deviations from linear trends. At larger tip-sample distances, the change in detector signal comes from far field scatter changes (e.g., background areas) of the cantilever axis and sample surface, and can be fitted to a linear far field background. The resulting difference (as discussed below with respect to fig. 2C) provides a relationship S _NF (d) 261 between the near field signal and the tip-sample distance, thereby enabling accurate access to the perpendicular near field response.

In another embodiment, a fast background removal algorithm may be used to fit the far field background signal directly from the scattered signal waveform in the time domain. The algorithm first extracts a short period (e.g., 120 mus) of the laser signal waveform around the bounce contact time t _s. Then in a short period (about 10 mus) before t _s, near field scattered light increases significantly with decreasing tip-sample distance. This short period is defined as the signal region, which corresponds to a short distance of tip-sample distance of substantially less than 5 nm. Before this signal region, the laser signal waveform exhibits a gradual and approximately linear increase due to the far field scattering background. A background trend fit (trend fit) may be performed on the region and then extrapolated to the signal region. The trend fit may be a polynomial function, e.g., a quadratic function, or other function selected such that it substantially overlaps with the scattering signal for large tip-sample distances, typically in the region above 10-20nm, 80-100nm, or less. The extrapolated far-field background is then used to subtract the light scattering of the signal region to obtain the pure near-field response. After far field background removal, the scattered signal may be averaged over a specified time window prior to t _s and used as a PF-SNOM signal. This means that in order to improve the signal-to-noise ratio (e.g. for a fixed spatial position and a fixed wavelength on the sample), the near field response can be averaged with the tip-sample distance based on an arithmetic average, i.e. the near field responses are added and summed to get the sum. In another embodiment, the scattered light signal may be averaged in the time domain before subtracting the background. In this case, the average data, i.e., the scattered light signal S (t) 207 of fig. 2A and the deflection signal D (t) 205 of fig. 2A, may be synchronized to overlap at the time of the synchronization reference point, which may be the bounce contact time t _s 210,210. After overlapping the data for each PFT period based on the time stamp, the near field data or deflection signal may be averaged. From this synchronous average data, a scattered light signal as a function of the distance S (d) 208 can be obtained as per the above procedure, and after background removal, a pure near field signal S _NF (d) 261 dependent on the tip-sample distance can be determined.

Fig. 2C shows a near field response 260, which may be determined from the integral of the PF-SNOM signal corresponding to curve 261 at a particular tip-sample distance d. This is indicated by the dark grey bars 262. By varying the distance d from which the near field response is extracted, near field signals corresponding to different values of d (e.g., different gating distances) can be obtained, thereby capturing a well-defined vertical near field response between the tip and the sample. Thus, data may be acquired at different distances d along different locations of the sample to produce an overall tomographic image of the sample. This example is shown and discussed in fig. 3A-3J below. Using the embodiment discussed with reference to fig. 1, a 256 x 256 pixel PF-SNOM image can be generated in about 30 minutes. In PF-SNOM imaging, an average signal of 50 or 150 peak force tap cycles per pixel can be used, depending on the signal intensity. The PF-SNOM spectra shown in FIGS. 3A-3C are collected by the scanning frequency of the tunable quantum cascade laser 128, which in this example is maintained at 2kHz. Each point in the PF-SNOM spectrum may be an average of about 400 PFT cycles. It should be noted that conventional tap-based s-SNOM cannot directly provide a distance dependent near field signal because its lock detection at different harmonics of the tap frequency only provides discrete near field signal values, and cannot provide the PF-SNOM tip-sample distance curve 261 (assuming no more complex reconstruction process is used for the near field response).

FIG. 2D is a graph 270 of the homodyne phase dependence of a PF-SNOM signal in accordance with an embodiment of the presently disclosed subject matter. As with conventional s-SNOM, the PF-SNOM signal can be interferometrically detected using a homodyne reference field (reference 124 in FIG. 1), which can be used to enhance near field signals and suppress background scattering in the tap mode s-SNOM. Fig. 2D shows PF-SNOM signal dependence at different homodyne phases 272 by adjusting the position of the reference retroreflector (REFERENCE RETROREFLECTOR). The reference retroreflector is part of an asymmetric michelson-type interferometer commonly used in s-SNOM, which is illustrated in fig. 1. Repeating again, in fig. 1, the QCL output beam is typically split by a beam splitter 121 to obtain a reference beam 124 by a QCL laser 128. When another portion of the laser output illuminates the parabolic mirror 120 and the needle tip 116, the reference beam 124 is reflected by a mirror or retroreflector and sent back to the beam splitter 121 and overlaps the needle tip-scattered light on the optical detector 123 after being focused by the focusing element 122. On an optical detector, the tip-scattered light, the reference light interference, and the recorded signal strength depend on the relative optical path length between the reference path and the tip-scattered path, i.e. the relative phase of the optical field. Intensity 271 in fig. 2D is the photodetector signal intensity when homodyne phase 272 (i.e., the relative optical path length between the tip-scatter optical path and the reference optical path) is adjusted. The intensity is typically varied by changing the position of the retroreflector in the reference path to obtain the clear signal minima and maxima shown in fig. 2D that are not disturbed by the light field. In another embodiment, the optical path length of the tip-scatter path is changed relative to a fixed reference path. As with the s-SNOM of the tap mode, the phase sensitive PF-SNOM can also be used to calculate the amplitude and phase of the near field signal and can extract the absorption and reflection of the sample from it.

Fig. 2E is a graph 290 showing different PF-SNOM signals at one wavelength (1405 cm ^-1) for different tip-sample distances when boron nitride nanotubes (Boron Nitride Nanotube, BNNT) are scanned over a 1000nm long line according to an embodiment of the presently disclosed subject matter. The morphology (e.g., three-dimensional representation) of BNNTs is shown in fig. 2F, and the null of the line scan starts from the BNNT end on the right side of the graph (near label "1"). In this example graph, response profiles of PF-SNOM extracted from the top surface of a Boron Nitride Nanotube (BNNT) sample are shown for different tip-sample distances d (profiles of d=4, 8, and 12nm are magnified by 2,4, and 8 times, respectively, for ease of comparison). Thus, images (e.g., two-dimensional representations) of different distances d may be extracted from this and other related maps of 256×256 pixel regions (or other suitable regions). We can see that when d decreases from 12nm to 1nm, the near field distribution along the BNNT nanotube top surface not only shows an overall larger near field signal as expected, but also more near field intensity near the nanotube end (near position "1" in fig. 2F), indicating that the BNNT end has stronger tip-sample interactions as the tip is closer to the surface. By fitting the vertical decay activity of the near field response with an empirical exponential decay function S (d) =a _NF e^(-d/b), where S (d) is the near field response depending on the tip-sample distance d, a _NF and b are fitting coefficients representing the total amplitude of the near field response and the vertical decay range, we can derive two new near field signal representations based on the total amplitude of the near field a _NF and the tip-sample characteristic 1/e decay range b. Direct acquisition of the tip-sample interaction range is a unique advantage of the PF-SNOM method, which is lacking for tapping mode s-SNOM with separate lock demodulation if no further reconstruction of the near field response is performed.

Another advantage of PF-SNOM over traditional tapping mode s-SNOM is the ability to directly acquire near field scatter signals and tip-sample perpendicular distance dependence at different distances (e.g. strobe sampling). This capability allows collection of tomographic near field images, which can reveal more microsecond tip-sample interactions than conventional s-SNOM techniques. As will be discussed below with reference to fig. 3A-3F, linewidth broadening (LINEWIDTH BROADENING) and resonant frequency shift of phonon polaron (Phonon Polariton, phP) resonances in boron nitride materials are observed with PF-SNOM over a tip-sample distance range of less than 10nm, whereas for s-SNOM in tapping mode, it is difficult to distinguish between this range since the required oscillation amplitude of the tip is typically 25-60nm, and subsequently the resulting complex signal (convoluted signal). Since a direct and quantitative elastic scattering signal can be obtained by PF-SNOM, the tip-induced relaxation behavior of PhP can be determined.

Since the PF-SNOM signal is proportional to the near field signal, the computational complexity required for numerical modeling of the PF-SNOM signal is much lower than for the tapping mode s-SNOM, where additional steps are required to interpret the tip oscillation and lock demodulation to reproduce the s-SNOM signal. Although the method of reconstructing s-SNOM by fourier synthesis is used in the tapping mode s-SNOM to reconstruct the tip-sample near field response vertically, the bandwidth of reconstructing s-SNOM is limited by the number of harmonic demodulation times and the tip oscillation amplitude in fourier synthesis. For example, even with 18 th harmonic demodulation in total, the vertical resolution in reconstructed s-SNOM is only 8.3nm for a tip oscillation amplitude of 150 nm. The 8.3nm vertical resolution does not capture the features of the short-range near-field interactions below 10nm that can be achieved by the system and technique of the present invention, and it is even more difficult to record 18 th order harmonics simultaneously without expensive high-end multichannel lock-in amplifiers. In contrast, the vertical resolution of PF-SNOM is related to the bandwidth of the infrared detector, PFT amplitude, and PFT frequency, and these parameters can be easily adjusted or met to improve vertical resolution. In our PF-SNOM device, the vertical resolution is estimated to be 0.12nm, so the near field resolution of PF-SNOM in the vertical direction is more accurate than existing tap mode s-SNOM techniques. A large number of tomographic images over a wide tip-sample distance can be obtained directly by PF-SNOM. This advantage can be used to reveal the three-dimensional near-field distribution of the plasmon nanoantenna. Furthermore, since spatial resolution depends on the lateral confinement of the field enhancement, PF-SNOM with high vertical accuracy can achieve the most stringent field confinement in gap mode (gap mode) by acquisition at short tip-sample distances and provide excellent 5nm lateral spatial resolution of the signal profile as shown in fig. 3I. Whereas in tapping modes s-SNOM exceeding 10-20nm the magnitude of the field limitation varies with the vertical oscillation of the tip, resulting in a compromised lateral field limitation.

The tomographic near field image and the SiC spectrum of BNNTs through PF-SNOM are of great interest for scattering near field optical microscopy. s-SNOM is widely used for characterization of polarized material near field response. Few have focused on the tip of the AFM changing the near field activity of the sample. In PF-SNOM, the near field response of short tip-sample distance is directly extracted, and the change of PhP spectral activity can be clearly observed. The metal tip not only detects the scatterer of the near field, but also acts as a damper (damper) over a short tip-sample distance. This means that the spatial pattern obtained by a scattering near field optical microscope should generally be treated with caution, since the measuring tip may affect the near field response being measured. Since PF-SNOM is able to obtain responses at different tip-sample distances, its measurement is particularly useful in interpreting actual near field responses.

As previously described, peak force tapping can not only enable topographical imaging, but also nanomechanical mapping and electrical imaging of sample properties (e.g., modulus or adhesion forces), such as determining nanoscale conductivity of a sample. In PF-SNOM, this approach can be combined with near field mapping to obtain correlated images of many sample properties. The ability to derive a perpendicular near field response from real-time measurement of near field scattering signals and the compatibility of PF-SNOM with electromechanical simultaneous measurements is achieved by explicit tip-sample contact in PFT mode. Since the AFM tip cantilever remains stationary, the kinetic energy stored in the cantilever is almost zero unless pushed up during dynamic contact. The cantilever thus responds very sensitively to intermolecular forces between the probe and the sample, and thus gives a definite bounce contact time t _s of the tip-sample zero distance reference point. In contrast, the tapping mode AFM cantilever is vibrated by external drive. Intermolecular forces between the probe and the sample cause a significant shift in the vibrational phase of the cantilever relative to the externally driven oscillation. While the phase shift in the tapping mode AFM is informative and is used as the phase imaging mode, the large phase shift can result in difficulty in determining the instantaneous tip-sample contact time for other AFM modes. The PF-SNOM can accurately determine the change in tip-sample distance over time, whereas the oscillatory phase shift in the tap mode AFM results in difficulty in implementing a time-gated detection scheme compared to the PF-SNOM.

In a tapping mode AFM, repulsive, attractive forces, and in particular, adhesion forces between the probe and the sample, result in nonlinear kinetic activity of cantilever vibration, which is exhibited even when high order lock-in demodulation is performed by non-harmonic far field scattering (anharmonic far-FIELD SCATTERING). In contrast, PF-SNOM measures the scattered signal directly from the side close to the PFT cycle, where it does not have any effect on the adhesion between the tip and the sample after contact, thus avoiding possible mechanical deformation of the adhesive surface. In this regard, PF-SNOM is more adaptable to rough and sticky samples than tap-mode s-SNOM. It should be noted that in another embodiment, a retraction curve (retract) may be used to obtain near field information, i.e. after point t _d of curve 205 in fig. 2A, the scatter signal is analyzed when the tip is separated from the surface. This can be achieved when the possible mechanical deformations are small or can be corrected.

PF-SNOM is a complement to existing peak force infrared (peak force infrared, PFIR) microscopes that measure laser-induced photo-thermal expansion in peak force tapping mode. PF-SNOM optically detects near field scattering signals from the tip and sample, which are determined by the tip-sample polarizability and the propagating surface wave; whereas PFIR performs mechanical detection based on the results of local optical absorption and subsequent dissipation of energy as heat. PF-SNOM inherits the advantage of s-SNOM in measuring rigid and polarized materials with spatial contrast due to differences in dielectric functions, compared to PFIR microscopy suitable for soft materials with large coefficients of photo-thermal expansion.

The PF-SNOM enables simultaneous mechanical, electrical and optical near field characterization of the sample. The three aspects of sample performance obtained by one measurement of PF-SNOM will be very helpful in studying nanoscale activities of functional materials, such as metal-insulator transitions of related electronic materials, and nanoscale optomechanical structures and devices. The universal compatibility of PF-SNOM makes it a more perfect scattering near-field optical microscopy platform.

Fig. 3A-3J show examples of valuable information available using tip-sample distance dependent near field spectroscopy of PF-SNOM. Fig. 3A-3I illustrate data example sets for analyzing formant peak locations and spectral peak widths of phonon polarons of Boron Nitride Nanotubes (BNNTs) and their tip-sample distance dependencies in accordance with embodiments of the subject matter disclosed herein. The PF-SNOM signals for three different tip-sample distances d were measured as a function of laser wavelength at three different spatial locations on the same BNNT nanotube (fig. 3A-3C show 1,2, 3, respectively, in fig. 2F). For example, fig. 3A shows the scattered near field response (y-axis 305) (1 nm 310, 3.5nm311, and 6.5nm 312 in this example) for a first location on BNNT at tip-sample distances of multiple wavelengths of the light source (x-axis 306). The lorentz fit (Lorentzian fittings) of the central peak region is shown as a solid line for the set of corresponding distance groups. The inset shows the full width transition of the fitted resonance peak omega _p at full-width half maximum (FWHM) at three different d values. It can be observed that the linewidth of ω _p increases with decreasing d.

Fig. 3B and 3C show similar curves for different positions relative to the sample. Thus, data corresponding to a 256x256 position matrix (e.g., pixels) may be collected, thereby ultimately generating a tomographic image based on the collected PF-SNOM data. Fig. 3D contains fitting parameters for the lorentz fitting of fig. 3A-3C. Fig. 3E shows simulated spectra and dielectric functions of Boron Nitride (BN) based on d=1, 3.5 and 6.5nm image dipole models. Fig. 3E illustrates the occurrence of the omega _p offset 320 at different values of d and is shown by an oblique vertical line. Similar shifts can be seen from the experimental data summarized in fig. 3D. Accurate measurement of plasma resonance and displacement based on tip-sample interactions provides a more accurate estimate of nanostructure resonance, which improves the assessment of spectral characteristics of polarized material based chemical sensors.

Fig. 3F-3G are diagrams of tomographic images that can be created from data collected by PF-SNOM techniques according to an embodiment of the presently disclosed subject matter. In the figure, a set of data corresponds to a near field response associated with a single tip-sample distance (e.g., d=1 nm in fig. 3F and d=4 nm in fig. 3G) for a single wavelength of light (e.g., 1390cm ^-1 in this example) from a light source. As previously described, surface phonon polarons (phps) are surface electromagnetic modes formed by the collective oscillations of optical phonons and the electric fields associated with the surface. It is known that polar materials such as silicon carbide (SiC) and Boron Nitride (BN) support the surface PhP. PF-SNOM is capable of detecting PhP in both the lateral and vertical directions of the sample surface. Fig. 3A-3I illustrate embodiments of data collection, measurement and image construction of Boron Nitride Nanotubes (BNNTs) using a PF-SNOM microscope.

The spatial resolution of PF-SNOM can be estimated from the edges of BNT. Fig. 3H shows an enlarged PF-SNOM image taken at d=1 nm. Fig. 3I shows a profile section of the PF-SNOM image along the white line 350 in fig. 3H, which achieves a spatial resolution of 5 nm. In contrast, the radius of the metal tip used in this example was estimated to be 30nm. The spatial resolution of PF-SNOM is greatly improved over the tip radius because of the gap-mode enhancement that occurs at short tip-sample distances of 1nm due to the highly non-uniform spatial distribution of the optical field, which is severely constrained in lateral dimensions to a range much smaller than the tip radius.

The spectral response of BNNTs also shows a dependence on the tip-sample distance d. FIGS. 3A-3C show the scattering spectra of PF-SNOM at three positions on BNT measured at three different d values of 1, 3.5 and 6.5nm at frequencies 1370cm ^-1 to 1440cm ^-1. The fitting parameters of the PF-SNOM spectra from three locations and three tip-sample distances are listed in fig. 3D, where it can be found that the center resonance frequency ω _p of PhP red shift (redshift) and its peak linewidth (in terms of full width at half maximum (FWHM)) narrows as the detection location gets farther from the nanotube end (from locations 1 to 3 in fig. 2F). This is most likely caused by interference between the tip-emitted PhP and the end-reflected PhP. PhP excited by lower frequencies has longer polarization wavelength and lower loss. Such lower frequency phps propagate farther and therefore will be more prominent at locations further from the tip. On the other hand, since lower polaron loss means longer lifetime, the linewidth of the resonance peak ω _p is correspondingly narrower.

In FIG. 3D, there are two special features that relate to tip-sample distance that can only be displayed by PF-SNOM. First, at the same location on the BNT, as the tip-sample distance d decreases, a small red shift in the resonance frequency ω _p of PhP occurs. This shift can be qualitatively explained by the image dipole (mage dipole model) model based on the dielectric function of boron nitride. Fig. 3E shows a simulated relationship between the maximum of the polarized resonance spectrum and the tip-sample distance d according to the image dipole model of a 30nm radius tip with a gold (Au) coating. In fig. 3E, a small displacement of 1cm ^-1 of ω _p was observed as the tip-sample distance d was reduced from 6.5 to 1 nm. Since the spatial frequency of the PhP depends on the frequency of the light source, the shift of ω _p indicates that in the high dispersion region of the PhP, the spatial pattern of the PhP varies at different measurement distances.

The second feature of FIG. 3D is that at the same probe location, the linewidth of ω _p widens as the tip-sample distance decreases, indicating that the lifetime of BNT-PhP decreases as the tip approaches the surface. The reduced lifetime may be due to the presence of a highly constrained gap mode that creates more relaxation channels that will greatly increase the optical density of states between the BNNT tip and the surface. Thus, while stronger field enhancement of the gap mode excites more PhPs, relaxation of PhPs is advantageous and the resonance linewidth is widened. This enhanced relaxation effect is conceptually similar to the fluorophore Bai Saier effect (Purcell effect) coupled to the resonator and the tip enhanced relaxation.

The novel PF-SNOM method and system achieves a number of advantages using the atomic force microscope system described above. In particular, PF-SNOM can rapidly measure three-dimensional near-field response. The PF-SNOM allows measuring multiple near field signals from multiple tip-sample distances. Thus, a three-dimensional near-field response cube (e.g., a three-dimensional map) may be constructed by stacking PF-SNOM images at different tip-sample distances into the data cube, or by aggregating near-field responses at different tip-sample distances from a set of two-dimensional lateral positions. In contrast, current tapping mode s-SNOM can achieve this operation at a sufficient speed only when highly complex algorithms are applied. Therefore, three-dimensional data mapping using conventional s-SNOM systems and methods is not feasible.

Another advantage over conventional solutions is that the ability to measure near field signals at tip-sample distances equal to or less than 2nm can improve spatial resolution. In PF-SNOM, the tip-sample distance can be accessed when the tip is very close to the sample (e.g., less than 2 nm). Thereby, a near field signal with a tip-sample distance of less than 2nm can be easily obtained. The minimum tip-sample distance possible is limited only by the detector response time. Measurements at a tip-sample distance of 1nm are demonstrated in the examples discussed above.

In contrast, in conventional tapping mode s-SNOM, an arbitrarily small oscillation amplitude of the AFM tip cannot be achieved because conventional tapping mode AFM requires at least a medium oscillation amplitude for AFM topography feedback. Typical conventional tapping mode AFM tip oscillation amplitudes are 25-60 nm. The signal from the tap mode s-SNOM cannot provide a near field signal between the tip and the sample within a small tip-sample distance range. In contrast, provided herein are PF-SNOM near field images at tip-sample distances of 1nm with high spatial resolution.

Another advantage is that the PF-SNOM amplifies the near field signal and increases the signal strength by gap mode boosting. The PF-SNOM allows conventional access slot mode enhancements. That is, when the metal tip is close to the conductor, or generally close to the sample where the real part of the dielectric function is negative, the electric field of the gap between the tip and the sample is greatly enhanced. The gap mode enhancement results in an electric field amplification and a stronger near field signal. PF-SNOM can measure near field scattering signals when the tip-sample is in close proximity (e.g., less than 2 nm). The close range of distances may enable collection of near field signals from gap mode enhancements without mixing with near field scattering signals lacking gap mode enhancements. Gap mode enhancement techniques can highly localize the excitation field and increase the spatial resolution of the PF-SNOM to about 5nm using an AFM tip of about 30nm radius. In contrast, conventional tapping modes s-SNOM provide spatial resolution in excess of 10nm.

Another advantage is that PF-SNOM uses simultaneous data acquisition that allows simultaneous averaging of multiple tip-sample approaches/retractions over multiple events, thereby improving signal-to-noise ratio. In PF-SNOM, data collection is synchronized with the change in tip-sample distance to the point immediately prior to tip-sample contact. Synchronous detection, also known as gated detection (gated detection), averages the near field signal, thereby improving the signal-to-noise ratio.

Another advantage over conventional s-SNOM is that PF-SNOM technology utilizes a peak force tapping mode instead of the conventional tapping mode. In the peak force tapping mode, the distance between the tip and the sample is predictable because the AFM cantilever does not store kinetic energy. In contrast, in the conventional tapping mode s-SNOM, the cantilever oscillates at a resonant frequency. Kinetic energy is stored in the AFM cantilever motion (KINETIC ENERGY). The interaction of intermolecular forces between the tip and the sample results in an unpredictable shift in oscillation phase in the tapping mode AFM. The change in the phase of tapping mode AFM oscillation means that the moment at which the tip and sample are closest cannot be predicted and is dependent on the sample surface. This results in difficulty in acquiring a time synchronization signal because the tip-sample distance cannot be predicted without knowing the basic sample profile to be measured.

PF-SNOM is not affected by this. In contrast, PF-SNOM accounts for the deviation of tip-sample distance due to intermolecular forces between AFM tip and sample. Intermolecular forces within a short tip-sample distance range cause the tip-sample distance to change during access to and retraction from the cantilever. In PF-SNOM, cantilever deflection is dynamically measured in synchronization with the near field signal. Cantilever deflection is used to correct the reading of tip-sample distance. In contrast, conventional tapping mode s-SNOM cannot correct for real-time tip-sample distance disturbances by using a lock-in amplifier.

Another advantage of PF-SNOM is the ability to measure near field signals, mechanical responses and electrical signals simultaneously in one AFM mode of operation without switching. In conventional s-SNOM, joint measurement of near field and mechanical mapping is done sequentially. That is, the peak force tapping mode may be used to determine mechanical information, but near field imaging is collected with conventional s-SNOM in the conventional tapping mode. Joint measurements are very time consuming. In PF-SNOM, both near field measurement and mechanical measurement are done in peak force tapping mode. Furthermore, the conductivity measurement may also be done in one mode of operation together with the near field imaging and mechanical mapping. Fig. 3J shows related measurements of sample morphology, mechanical modulus, contact current, and near field response of hexagonal boron nitride flakes on a semiconductor silicon substrate. Hexagonal boron nitride has a higher modulus and lower electrical conductivity than silicon substrates. The near field response of phonon polarons in hexagonal boron nitride at an infrared illumination frequency of 1530cm ^-1 is shown.

In another advantage, PF-SNOM provides a higher signal-to-noise ratio per unit tip-sample oscillation period than conventional tapping mode s-SNOM. In PF-SNOM, the near field signal can be restored to the integral of the near field signal over a tip-sample distance range. This may provide more data points than single-value lock-in demodulation. Thus, fewer periods of tip oscillation are required compared to the conventional tapping mode s-SNOM.

Another advantage is that the peak force tapping mode on which PF-SNOM is based is widely applicable to a range of samples. The tapping mode atomic force microscope provides poor or unstable feedback on sticky or rough sample surfaces. Thus, the tapping pattern s-SNOM cannot be applied to these sample surfaces. The peak force tapping mode AFM does not have as much limit on the viscosity or roughness of the sample surface. Thus, PF-SNOM inherits the broad applicability of peak force tapping modes, and is applicable to non-ideal sample surfaces.

FIG. 4 is a flow chart 400 illustrating a method suitable for implementing PF-SNOM techniques for AFM microscopy, in accordance with an embodiment of the subject matter disclosed herein. The method may begin at step 410, where a sample is placed on a sample stage of an AFM and a PF-SNOM scanning cycle is initiated at step 410. In one embodiment, as described above, the sample may be BNNT. When the PF-SNOM process is initiated, the piezo-electric drive stage may generate a signal configured to induce a motion on the sample stage that is a periodic variation in the vertical distance between the proximity tip/cantilever device and the sample. The tip may then be maneuvered toward the sample to a particular location (e.g., pixel location) in step 415. This will cause an interaction between the tip and the sample and a vertical deflection of the cantilever, resulting in a dynamic contact of the tip with the sample at the oscillation frequency of the piezoelectric material in the sample stage. As mentioned above, this frequency is typically between 0.1kHz and 100.0 kHz.

When the tip interacts with the sample, the method determines near field responses for various distances (e.g., strobing discrete distance responses) in step 420. A plurality of tip-sample distances is determined by detecting vertical deflection of the cantilever, the tip-sample distances corresponding to the tip in contact with the sample and the deflection of the cantilever over a period of time. That is, as the maximum deflection moves away from the rest position, the bouncing contact may be determined within a certain time interval. In this manner of determination, a plurality of near field scattering responses may be determined from light focused on the sample at the tip contact region of the sample. In addition, any background signal may be removed from the response signal initially determined to be representative of the background signal when the tip is not sufficiently close to the sample to cause a short-range near-field interaction during a periodic change. Then, a linear or nonlinear response may be provided corresponding to the background signal, and when the sample induces a deflection in the cantilever through the induced interaction, then an approximate linear or nonlinear response may be removed from the plurality of near field scattering responses.

These scans can be done at different wavelengths. Thus, in step 430, an interrogation is provided to scan at another frequency. If scanning is to be performed at the pixel location at an additional frequency, the method returns to step 420 after adjusting the wavelength of the light source in step 440 and the scattered near field response is again recorded using the new wavelength. If there are no more wavelengths at that location for which response data for the sample can be collected, the method proceeds to query step 445 to determine if more pixel locations are to be analyzed. If so, the method returns to step 415 and moves the needle tip to the new pixel location. If there are no more pixel locations at query step 445, the method moves to step 460 where all of the collected data may be used to generate one or more tomographic images of the underlying sample. This may be achieved by correlating multiple near field scattering responses with multiple tip-sample distances for each sample location to generate a near field response data map of the sample. The correlation function may further include: a set of near field scattering responses from the plurality of near field scattering responses is associated with the tip-sample distance for each sample location, wherein each set is associated with an equivalent tip-sample distance of d = 1 to n nanometers for each sample location. Furthermore, such correlation may be achieved at different wavelengths used to analyze the sample. Fig. 4 depicts different examples such as a near field mapping/imaging of constant wavelengths, near field point spectra of various wavelengths at a single spatial location, and near field spectra of various wavelengths at different spatial locations (e.g., a line scan or hyperspectral map of 256 x 256 pixels, where the full spectrum is recorded at each pixel).

Conventional s-SNOM based on tapping mode AFM operation requires a continuous-wave or quasi-continuous wave light source, i.e. if a pulsed light source, a sufficiently high repetition rate, typically in the MHz range of 10s, e.g. 80MHz. The reason for this is that the near field signal is obtained by demodulating the tip scattering signal at higher harmonics (typically the 2-4 th harmonics) of the tip oscillation frequency (typically 200-400 kHz). The light source repetition frequency in the range of-100 kHz to-1 MHz is typically lower than the Nyquist sampling rate (Nyquist SAMPLING RATE) required to reveal higher harmonics of the tip oscillation frequency, and therefore demodulation typically performed using a lock-in amplifier in s-SNOM will be unsatisfactory. In order for a conventional s-SNOM to work with a low repetition rate laser, a more complex signal reconstruction must be performed. PF-SNOM requires less stringent light sources. Since the scatter signal in the PF-SNOM is typically extracted only within a few tens of microseconds before establishing tip-sample contact around the bounce contact time t _s (see fig. 2A and 2B), it is sufficient to illuminate the sample only during this time interval. This means that in the extreme case, the laser only needs to emit during about 50us in a PET period at a PFT frequency of 2kHz, which can typically last 500 us. In this example, a 10% reduction in duty cycle may be advantageous to prevent overheating of the sensitive sample. Furthermore, light source pulses in the range from kHz up to MHz still allow PF-SNOM data to be extracted. Since the tip position in the PFT cycle is known and well-defined at each instant, the optical detector signal can reference a specific tip position. For low laser repetition rates (e.g., 2 kHz) of the PFT cycle frequency sequence, only a few pulses (e.g., only 1) per cycle are recorded with the tip position. A sufficient number of data points of the scattering signal versus tip-sample distance S (d) can ultimately be achieved by collecting data over multiple PFT cycles so that the curve 208 in fig. 2B, which consists of discrete data points, can be interpolated and analyzed. The laser repetition rate and PFT frequency may be synchronized with each other so that a scattering signal at a certain fixed tip-sample distance (e.g. d=1 nm) may be obtained in each PFT period. In the special case of such synchronous PFT periods and laser repetition frequencies, once the shape of the background signal is determined, the PF-SNOM signal subtracted from the background signal can be inferred by measuring only a single photodetector signal during a single PFT period. This means that the entire curve of the scattering signal S (d) as a function of tip-sample distance need not be determined and that a low kHz pulsed laser can be used. It requires knowledge of the background signal, which can be obtained by measuring the scattering signal to tip sample distance (curve 208 in fig. 2B), for example, by moving the relative time between the synchronized laser pulses and the PFT period, or by operating out of synchronization, so that enough data points are collected to interpolate and reconstruct curve 208 in fig. 2B. As previously described, a subsequent linear or nonlinear fit will produce a background curve. This also requires that the background shape does not change between different levels in the imaging or spectrum.

For PF-SNOM, there are several advantages to being able to use a continuous wave light source like a conventional tapping mode s-SNOM. As described above, if the sample is sensitive to light or heat, the duty cycle and time at which the sample is illuminated can be minimized. This prevents the sample from being destroyed or otherwise modified unnecessarily. In addition, PF-SNOM can use more light sources than s-SNOM due to the more flexible repetition frequency range. For example, s-SNOM cannot use a 1-100kHz optical parametric amplifier system in the mid-infrared region, while PF-SNOM can be used.

In alternative embodiments, PF-SNOM may employ a broader wavelength range outside of the mid-infrared spectrum region, such as the ultraviolet, visible, near infrared, and terahertz or far infrared ranges. QCL, optical parametric oscillator (optical parametric oscillator, OPO) and amplifier exist as pulsed and continuous wave sources in the infrared. Ultraviolet, visible and near infrared rays are covered by laser sources such as solid state lasers, diode lasers, fiber lasers, OPO or gas lasers, and laser sources based on nonlinear frequency conversion including optical parametric generation, sum frequency generation, harmonic generation, frequency comb and related methods. In the terahertz spectral region, terahertz quantum cascade lasers are present, whereas terahertz gas lasers, terahertz antennas or free electron lasers are already present to cover this range.

Another embodiment is adapted to perform near field spectroscopy using a broadband light source, such as a laser driven plasma source, a silicon carbide rod (globar), a supercontinuum source, or a synchrotron. These sources may cover hundreds of cm ^-1 at a time, while QCL provides a narrow laser line typically about 1cm ^-1 in width. Pulses of tens to hundreds of cm ^-1 provided by a broadband optical parametric oscillator or amplifier are also sufficient. When the laser is replaced with a broadband light source, the setup is the same as in fig. 1. But now a PF-SNOM near field interferogram is obtained. This is achieved by varying the relative path length between the reference arm 124 and the arm including the needle tip 116 in the asymmetric michelson interferometer of fig. 1. Typically, this is accomplished by moving (e.g., using an electrically powered platform) the retroreflectors in reference path 124. The PF-SNOM signal is extracted according to the above steps while changing the relative path length. In an embodiment, the path length is changed stepwise and after each step the PF-SNOM signal is obtained at a specific tip-sample distance d (e.g. d=1 nm) and possibly an average of the number of specific PFT cycles. The resulting dataset contains an interferogram, i.e. the PF-SNOM signal at a specific distance d is a function of the relative path lengths of the two interferometer arms. The subsequent fourier transform yields the PF-SNOM near field spectrum as a function of wavelength. This process can be used to acquire spectra from broadband sources. In various embodiments, the path length is continuously varied rather than stepwise.

In the above PF-SNOM embodiment, the distance between the AFM tip and the sample is periodically oscillated by adjusting the position of the sample, and in addition, the same distance oscillation effect can be obtained by oscillating the position of the AFM tip. In this embodiment, the position of the AFM tip can be driven from outside at a lower mechanical resonance frequency than the cantilever, and the associated near field signal and tip-sample distance measurements can be performed using PF-SNOM. It should be noted that the tip movement in this embodiment is different from the resonant oscillation of the cantilever in the tapping mode s-SNOM. In PF-SNOM, the oscillation of the position of the AFM tip driven at the resonance frequency of the AFM cantilever is avoided. Under PF-SNOM operation, the cantilever does not store kinetic energy in the form of resonant oscillations. In contrast, in the s-SNOM in the tapping mode, the cantilever is driven to oscillate at its resonance frequency. As a result, cantilever vibrations undergo a phase change upon interaction with the sample, which makes it difficult to determine the tip-sample distance at a given time.

Fig. 5 is a drawing showing elements or components that may be present in a computer device or system configured to implement a method, process, function, or operation in accordance with an embodiment. In accordance with one or more embodiments, a system, apparatus, method, process, function, and/or operation is provided for configuring and efficiently presenting a user interface to a user in accordance with a user's prior behavior, in whole or in part, in the form of a set of instructions executable by one or more programmed computer processors (e.g., a Main Control Unit (MCU), a Central Processing Unit (CPU), or a microprocessor). Such processors may be incorporated into devices operated by or in communication with other components of the system, servers, clients, or other computing or data processing devices. By way of example, FIG. 5 is a drawing showing elements or components that may be present in a computer device or system 600 for implementing a method, process, function or operation in accordance with an embodiment. The subsystems shown in fig. 5 are interconnected via a system bus 602. Additional subsystems include a printer 604, a keyboard 606, a fixed disk 608, and a display 610 coupled to a display adapter 612. Peripheral devices and input/output (I/O) devices coupled to I/O controller 614 may be connected to the computer system by any number of means known in the art, such as serial port 616. For example, serial port 616 or external interface 618 may be used to connect computer device 600 to other devices and/or systems not shown in fig. 5, including a wide area network such as the internet, a mouse input device, and/or a scanner. Interconnection via system bus 602 allows one or more processors 620 to communicate with each subsystem and control the execution of instructions stored in system memory 622 and/or fixed disk 608, as well as the exchange of information between the subsystems. The system memory 622 and/or the fixed disk 608 may include tangible computer-readable media.

In this embodiment, the AFM 105 may also be coupled to the bus 602 via an interface (not shown). Thus, the operations and processes described above may be initiated and performed using the processor 620 of the overall computing system 600 or the onboard processor 621 of the AFM 105. Further, the data determined and collected by the AFM 105 may be stored in the memory 622 of the computing system 600 or may be stored in the local memory 623 associated with the AFM 105.

It should be appreciated that the present disclosure as described above may be implemented in the form of control logic in a modular or integrated manner using computer software. Based on the disclosure and teachings provided herein, one of ordinary skill in the art will appreciate other ways and/or methods of implementing the present disclosure by hardware as well as combinations of hardware and software.

Any of the software components, processes, or functions described in the present application may be implemented as software code which may be executed by a processor using any suitable computer language (e.g., assembly language Java, javaScript, C, C ++ or Perl) and using, for example, conventional or object-oriented techniques. The software codes may be stored as a series of instructions or commands on a computer readable medium, such as a Random Access Memory (RAM), a Read Only Memory (ROM), a magnetic medium such as a hard disk drive or a floppy disk, or an optical medium such as a CD-ROM. Any such computer-readable medium may reside on or within a single computing device and may reside on or within a different computing device within a system or network.

All references, including publications, patent applications, and issued patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and/or were set forth in its entirety herein.

The use of The terms "a" and "an" and "The" and similar referents in The specification and The appended claims are to be construed to cover both The singular and The plural, unless otherwise indicated herein or clearly contradicted by context. The terms "having," "including," "comprising," and the like in the description and in the appended claims, unless otherwise specified, are to be construed as open-ended terms (e.g., meaning "including, but not limited to"). Unless otherwise indicated herein, the recitation of numerical ranges herein are merely intended to serve as a separate reference to each separate value falling within the range, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. Unless otherwise indicated, any and all examples, or exemplary language (e.g., "such as") provided herein, is intended merely to better illuminate the embodiments and does not pose a limitation on the scope of the disclosure. No language in the specification should be construed as indicating any non-claimed element as essential to every embodiment of the disclosure.

There may be different arrangements of parts, and there may be parts and steps not shown or described, than shown in the drawings or described above. Similarly, some features and subcombinations may be of benefit and may be employed without reference to other features and subcombinations. The embodiments are by way of example only and not for purposes of limitation, and alternative embodiments will be apparent to the reader of this patent. Accordingly, the present subject matter is not limited to the embodiments depicted above or in the drawings, and various modifications may be made to the embodiments without departing from the scope of the appended claims.

Claims

1. A method of measuring optical properties of a sub-micron region of a sample, the method using an atomic force microscope, the method comprising:

allowing the probe to interact with the sample;

illuminating the sample with a beam of light from a radiation source such that light is scattered from the probe-sample interaction region;

Collecting scattered light from the probe-sample interaction region and a background region using a detector, the scattered light being a function of a distance between the probe and the sample; and

Constructing a near field signal in response to the collected scattered light relative to the distance; and

Wherein the vertical resolution of the near field signal is at least 7nm.

2. The method of claim 1, wherein constructing the near field signal further comprises:

extrapolation of a linear function of a distance dependent scattered light response when the scattered light is dominated by scattered light from the background region of larger tip-sample distance; and

When the scattered light is not branched by the scattered light from the background region of smaller tip-sample distance, the extrapolated linear function is subtracted from the scattered light.

3. The method of claim 1, wherein constructing the near field signal further comprises:

extrapolating a quadratic function of the distance-dependent scattered light response when the scattered light is dominated by scattered light from the background region of greater tip-sample distance; and

When the scattered light is not branched by the scattered light from the background region of smaller tip-sample distance, the extrapolated quadratic function is subtracted from the scattered light.

4. The method of claim 1, wherein constructing the near field signal further comprises:

Extrapolation of a polynomial function of a distance-dependent scattered light response when the scattered light is dominated by scattered light from the background region of greater tip-sample distance; and

When the scattered light is not branched by the scattered light from the background region of smaller tip-sample distance, the extrapolated polynomial function is subtracted from the scattered light.

5. The method of claim 1, further comprising: a tomographic section of a spatial near field response map of the sample is determined for a plurality of tip-sample distances for a plurality of locations of the sample.

6. The method of claim 1, further comprising: creating a spatial near field response map for at least one specific vertical tip-sample distance for a plurality of locations on the sample, wherein at least one map has a spatial resolution of 20nm or better.

7. The method of claim 1, further comprising: creating a spatial near field response map for at least one specific vertical tip-sample distance for a plurality of locations on the sample, wherein at least one map has a spatial resolution of 5nm or better.

8. The method of claim 1, wherein the vertical resolution of the near field signal is at least 1.

9. The method of claim 8, wherein a spatially resolved near field response map is created for at least one particular vertical tip-sample distance, and wherein the map comprises at least 100 x 100 pixels and is completed in less than 30 minutes.

10. The method of claim 1, further comprising: the wavelength of the radiation source is changed to determine a near field spectrum corresponding to the dependence of near field scattering on wavelength.

11. The method of claim 1, further comprising: a bounce contact time ts corresponding to zero tip-sample distance is determined as a synchronization point, whereby the tip-sample distance from a probe deflection signal can be predictably determined and correlated with the signal of the scattered light.

12. The method of claim 1, further comprising: a separation time td corresponding to the tip-sample distance no longer being zero is determined to be used as a synchronization point so that the tip-sample distance from the probe deflection signal can be predictably determined to be correlated with the signal of the scattered light.

13. The method of claim 11, wherein the near field signal comprises a plurality of periods that are synchronously averaged, thereby improving signal-to-noise ratio.

14. The method of claim 1, further comprising: the signal of the scattered light is interferometrically amplified at an optical detector using an optical interferometer.

15. The method of claim 1, wherein the wavelength of the light source comprises a range from ultraviolet wavelengths to far infrared wavelengths.

16. The method of claim 1, wherein interacting the probe with the sample further comprises: the probe is caused to interact with the sample in a peak force tapping mode.

17. An atomic force microscope for measuring optical properties of a sub-micron region of a sample, comprising:

a probe for interacting with the sample;

A radiation source for illuminating the sample with a beam of light such that light is scattered from the probe-sample interaction region;

A detector for detecting scattered light from the probe-sample interaction region and a background region, the scattered light being a function of the distance between the probe and the sample; and

A processor constructs a near field signal in response to the detected scattered light relative to the distance, and wherein a vertical resolution of the near field signal is at least 7nm.

18. The AFM of claim 17, further comprising a spatial near field response map for at least one particular vertical tip-sample distance for a plurality of locations on the sample, wherein at least one map has a spatial resolution of 20nm or better.

19. The AFM of claim 17, further comprising a spatial near field response map for at least one particular vertical tip-sample distance at a plurality of locations on the sample, wherein at least one map has a spatial resolution of 5nm or better.

20. The method of claim 17, wherein the vertical resolution of the near field signal is at least 1nm.